Definitions - Y1S1 Flashcards by 0a548ck Kan3

Q

Roots of unity

A

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Q

Order of a root of unity

A

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Q

Primitive root of unity

A

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Q

Prime number

A

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Q

Lcm, gcd

A

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Q

Congruent modulo n

A

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Q

Congruence classes

A

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Q

Congruence equations

A

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Q

Groups of units

A

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Q

A

Number of integers

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Q

Sets

A

A collection of elements

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Q

Cartesian product

A

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Q

Functions

A

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Q

Graph of a function

A

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Q

Identity map

A

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Q

Composition

A

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Q

Inverse

A

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Q

Function spaces

A

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Q

Image of a function
(Compare 2 sets as well)

A

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Q

Injective

A

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Q

Surjective

A

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Q

Bijective

A

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Q

Left and right inverse

A

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Q

Finite set

A

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Q

Cardinality

A

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Q

Countable sets

A

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Q

Equivalence relation

A

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Q

Equivalence classes

A

Q

Partition of a set

A

Q

The set of permutation on n letters

A

Q

Cyclic permutations / cycle

A

Q

Transposition

A

Q

Even and odd permutations

A

Q

Sign of a permutation

A

Q

Field

A

Q

Additive group

A

Q

Ring

A

Q

Commutative ring

A

Q

Integral domains

A

Q

Polynomials in x

A

Q

Equal polynomials

A

Q

Addition of polynomials

A

Q

Multiplication of polynomials

A

Q

A

With coefficients in f

Q

Leading coefficients

A

Q

Degree of f

A

Q

Monic

A

If the leading coefficient is 1

Q

Irreducible polynomials

A

Q

lcm of a polynomial

A

Q

gcd of a polynomial

A

Q

Equal matrices

A

Q

A

Wrong way around (too obvious to change)

Q

Compact matrix multiplication

A

Q

A

Q

Invertible matrix

A

Q

Linear maps associated with a matrix
Include formula

A

Q

Linear map

A

Q

Row Echelon form

A

Eg the 0 matrix

Q

RREF

A

Q

Linear subspace

A

Q

Null space of a matrix

A

Q

Basis of a linear subspace

A

Q

Standard basis

A

Q

Nullity of a matrix

A

Q

Rank of a matrix

A

Q

Transposition

A

Q

Dot product / the angle

A

Q

Euclidean length
Euclidean distance

A

Q

Orthogonal matrix

A